Wagering Game That Allows Player to Alter Payouts Based on Equity Position

ABSTRACT

A wagering game that allows a player to adjust a positive expectation game situation to a lower expectation game situation. In return, the player can increase the paytable so that awards the player wins will be paid at a higher rate. Alternatively, the player can increase the paytable in exchange for a less favorable game state.

CROSS REFERENCE TO RELATED APPLICATIONS

This application is a continuation of part of application Ser. No.10/874,558, now allowed, which both 1) claims benefit to provisionalapplication 60/548,481, and 2) is a continuation in part of applicationSer. No. 10/688,898, now U.S. Pat. No. 7,163,458; all three applications(Ser. Nos. 10/874,558; 60/548,481; 10/688,898) are incorporated byreference herein in their entireties. This application is also acontinuation in part of application Ser. No. 11/158,919, now pending,which is incorporated by reference herein in its entirety.

This application is also related to U.S. Pat. No. 7,294,054 which isincorporated by reference herein in its entirety. This application isalso related to application Ser. No. 10/754,587, which is incorporatedby reference herein in its entirety. This application is also related toapplication Ser. No. 11/379,561, which is incorporated by referenceherein in its entirety. This application is also related to applicationSer. No. 11/379,555, which is incorporated by reference herein in itsentirety. This application is also related to application Ser. No.11/738,455, which is incorporated by reference herein in its entirety.

FIELD OF THE INVENTION

The present inventive concept relates to a wagering game that allows aplayer to alter payouts based on an equity position the player has inthe wagering game.

DESCRIPTION OF THE RELATED ART

Casino wagering games are a billion dollar industry. When a player isplaying a wagering game such as video poker or craps, the player may belimited to a single paytable.

What is needed is a manner in which a player can have an opportunity toreceive a different paytable.

SUMMARY OF THE INVENTION

It is an aspect of the present general inventive concept to provide aplayer an opportunity to exchange game states for a different paytable.

The above aspects can be obtained by a method that includes (a)receiving a wager from a player on a player chosen outcome, the wagerpaying according to a first paytable; (b) conducting a wagering gamewith a first game state; (c) progressing the first game state into asecond game state based on a random determination; (d) determining fromthe player that the player wishes to change from the second game stateback into the first game state in exchange to activate a second paytablefor the wager; (e) reverting the game from the second game state back tothe first game state; (f) completing the game to determine whether thewager wins or loses; and (g) if the wager is determined to win, thenpaying the wager according to a second paytable, (h) wherein if theplayer did not choose to change from the second game state back to thefirst game state, then if the wager is determined to win, then the wageris paid using the first paytable.

These together with other aspects and advantages which will besubsequently apparent, reside in the details of construction andoperation as more fully hereinafter described and claimed, referencebeing had to the accompanying drawings forming a part hereof, whereinlike numerals refer to like parts throughout.

BRIEF DESCRIPTION OF THE DRAWINGS

Further features and advantages of the present invention, as well as thestructure and operation of various embodiments of the present invention,will become apparent and more readily appreciated from the followingdescription of the preferred embodiments, taken in conjunction with theaccompanying drawings of which:

FIG. 1 is a flowchart illustrating one example of a wagering game,according to an embodiment;

FIG. 2 is a flowchart illustrating one example of borrowing money to payfor a wager, according to an embodiment.

FIG. 3 is a flowchart illustrating an exemplary method of storingpositive expectations for later use, according to an embodiment;

FIG. 4 is block diagram illustrating an exemplary set of components inorder to implement an embodiment;

FIG. 5 is a flowchart illustrating an exemplary method of making aconditional wager, according to an embodiment;

FIG. 6 is a flowchart illustrating an exemplary method of using equityin a first wager in progress in order to fund a second wager, accordingto an embodiment; and

FIG. 7 is a flowchart illustrating an exemplary method of adjustingpayouts based on a change in game position, according to an embodiment.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

Reference will now be made in detail to the presently preferredembodiments of the invention, examples of which are illustrated in theaccompanying drawings, wherein like reference numerals refer to likeelements throughout.

Reference will now be made in detail to the presently preferredembodiments of the invention, examples of which are illustrated in theaccompanying drawings, wherein like reference numerals refer to likeelements throughout.

The present invention relates to casino games with a feature allowing aplayer to borrow money from the house. The loan is not made inaccordance with known procedures for borrowing money in a casino, suchas applying for credit and receiving a marker or other cash loan towager with.

The present invention allows a player to borrow money against theplayer's position in a game already in progress. Some casino games areover immediately (i.e. “casino war,”) in which there is really no “inprogress” state. Other games, such as games related to betting onprogressions, contain a plurality of game states or intervals upon whicha player can develop a “positive position.” A game related to betting ona progression can comprise a game which has numerous game states,typically with a preferred outcome. A positive position can comprise agame in a particular game state, with or without particular currentwagers made, wherein the player has a better than 100% expected return.

In a first embodiment of the present invention, the player can borrowmoney from the house when the player is in a positive expectationposition.

For example, consider a simple game wherein piece A and piece B start ata beginning square are advanced around a 20 square field according torespective rolls of dice, wherein a winner is the piece which reaches afinish area first. If the first three rolls for piece A are 1, 2, 1,then piece A would be at square number 4. If the first three rolls forpiece B are 5, 6, 3, then piece B would be at square number 14.Obviously, piece B has a much better chance of winning the game thanpiece A. If a wager was made on piece B before the race began (assumingeach piece pays even money to win), then piece B is considered to have apositive expectation.

A “loan” to the player can be made based on this positive expectation.If the player loses, he typically will not be required to pay the loanback. If the player wins, then the player pays back the loan. However,in exchange for the privilege of taking such a loan out, the player maythen also have to pay some type of “interest,” commission, vigorish,etc., to the house for the loan.

In an embodiment of the present invention, a player may borrow moneyfrom the house if the player is in a positive expectation position andthe player makes particular bets wherein the player ensures that he orshe is guaranteed to make a profit regardless of an outcome of the game.

For example, consider a bidirectional linear progression game, wherein apiece moves in either of two opposing directions, wherein the game endswhen the piece reaches either a leftmost side or a rightmost side.Consider the following exemplary conditions (of course other types ofgames and conditions can be used besides the one in this example): thereare three squares (numbered −1, 0, +1) with finish squares to the veryleft and right, with one piece moving in either linear direction (leftor right) based on a roll of a six sided die (with sides −1, −1, −1, +1,+1, +1, or L, L, L, R, R, R). If the die rolls a −1 (or L), then thepiece moves one square to the left. If the die rolls a +1 (or R), thenthe piece moves one square to the right. When the piece reaches to thefinish square left of the leftmost square, or to the finish square tothe right of the rightmost square the game is over and either left orright has won. When the piece is on the −1 square, betting on right pays3:1 and betting on left pays 1:3. When the piece is on the +1 square,betting on right pays 1:3 and betting on left pays 3:1. When the pieceis on the 0 square, betting on left or right pays 1:1. Of course thenumber of squares, parameters of the die, payouts, etc. can be set towhatever the game designer prefers. Further, note that for simplicitythis variation has no house edge, although of course a house edge can beworked into the game.

Table I Illustrates an example a game sequence of the above-describedgame. Each operation can comprise rolling the dice and/or making awager.

TABLE I Bet Left Right Exp. Oper. Action Result Position Placed Win WinProfit 0 Start n/a 0 n/a $0 $0 $0 1 Roll R +1 n/a $0 $0 $0 2 Wager n/a+1 $5 left  $15 −$5 $0 3 Roll L 0 n/a $15 −$5 $5 4 Roll L −1 n/a $15 −$5$10 5 Wager n/a −1 $5 right $10 $10 $10 6 Wager n/a −1 $5 right $5 $25$10 7 Wager n/a −1 $5 right $0 $40 $10 8 Roll R 0 n/a $0 $40 $20 9 RollR +1 n/a $0 $40 $30 10 Roll R Right Win n/a $40

In operation #0, the game starts. The puck is placed on the centerposition (position 0)). No bets are made yet.

Now the game proceeds to operation 1, which is a roll. The result of theroll is R. Thus the puck is moved 1 square to the right and is now onposition +1. No bets have been made, so if right wins or left wins theplayer wins $0.

The game then proceeds to operation 2, wherein the player makes a wager.The player makes a $5 wager on the leftmost side (although of course theplayer can choose the amount to wager and the event wagered on). If theleftmost side wins, the player wins $15, while if the rightmost sidewins, the player wins −$5 (loses $5). There is no expected profit (orloss) for the player (since this example has no house edge).

The game then proceeds to operation 3, wherein the die is rolled with anoutcome of L. Thus, the puck is moved from +1 to 0. Note that theexpected profit is now $5, since the puck moved closer to the left whichis the outcome that the wager was placed. Thus, the player expectationof this game state is now $5, because in the long run the average amountthe player will win is $5. Since this number is positive, the house willlose from this game state in the long run.

The game then proceeds to operation 4, wherein the die is rolled with anoutcome of L. The puck moves from 0 to −1. Note that the expected profitis now $10, since the puck has moved closer to the left. This game stateis even more favorable to the player and the player's wager than theprevious game state.

The game then proceeds to operation 5, wherein the player places a $5wager on the right. Note that is the puck reaches the leftmost side theplayer wins $10, and if the puck reaches the rightmost side, the playerwins $10. Thus, the player is now in a guaranteed winning situation.

The game then proceeds to operation 6, wherein the player places a $5wager on the right. Now if the rightmost side wins the player wins $25,while if the leftmost side wins the player wins $5.

The game then proceeds to operation 7, wherein the player places a $5wager on the right. Now if the rightmost side wins the player wins $40,while if the leftmost side wins the player wins $0 (breaks even from allof the bets).

The game proceeds to operation 8, wherein the die is rolled and theoutcome is R. The puck is moved to the right one square to position 0(the middle). The expected profit is now $20.

The game then proceeds to operation 9, wherein the die is rolled and theoutcome is R. The puck is moved to the right one square to position 1.The expected profit is now $30.

The game then proceeds to operation 10, wherein the die is rolled andthe outcome is R. The puck is moved one square to the right which placesthe puck to the right of position 1, which ends the game. The rightmostside has won. The expected profit is now $40, since the player wins aprofit of $40 (actually win $60 but has bet $20) and the game is over.

Note that the player has placed $20 in bets (4 bets of $5). However, theplayer could have started with only $5 in capital, which was wagered inoperation 2. Upon reaching operation 5, the house could “lend” theplayer $5 with which to bet with. This is because the player is puttinghimself or herself into a guaranteed winning position by making thiswager. Upon place the wager in operation 5, the player is guaranteed anet profit $10 regardless of which side wins. Thus, the house can makethis “loan” to the player since the house is guaranteed to get paid backonce the game is over. Thus, this wager can be made from the player'sown funds or from a “loan” from the house—the end result should still bethe same.

The same principle applies to the wagers made in operations 6 and 7. Thewager in operation 6 results in both outcomes resulting in a profit,thus the house is guaranteed to recoup the loan once the game is over.In operation 7, the player breaks even if the leftmost side wins. Thus,if the leftmost side wins, the player pushes, as whatever he wins fromhis or her bets on the leftmost side offset the losses from bets on theother side. The house can “lend” the player the money to make the wagerin operation 7 because the player is guaranteed to at least break even,thus paying back whatever loan was made.

Therefore, it is noted that according to an embodiment, the player canbegin a game with a finite amount of money, and parlay his or her moneyinto an infinite (in theory) amount of money during the same game. Forexample, in the above example, if the game did not end in operation 10but instead the puck traveled back to the left (one or two squares), theplayer can then make further wagers to increase the amount of his or herwin.

In some situations, the player may make a wager which will not put theplayer into a guaranteed winning situation. However, if the playerincreases that wager, the player may then put himself into a guaranteedwinning situation. For example, in the above example, if the wager inoperation 5 is $1 (instead of $5), this would result in a net win of $12for the leftmost side and a net loss of $2 for the rightmost side.However, if the player wagers $2, then this would result in a net win of$13 for the leftmost side and a net push if the rightmost side wins.Thus, the house may allow the player to make at least a $2 wager inoperation 5 (on the rightmost side), since this would result in ano-lose situation for the player (hence the house will always collectthe “loan”). But the house may not wish to allow the player to make the$1 wager (unless of course the player is using his or her own money),since there may be a situation where the player will not be guaranteedto pay this loan back.

Thus, the house may wish to compute at what amount a player should makea particular wager in order to be allowed to bet with “borrowed” money.Of course, if the player is not currently in an “equity” state in thegame, then no wager (on either side) would put the player into aguaranteed winning situation. An equity state of the game can beconsidered a position where a player has a positive expectation based onhis or her wagers and the game state. A player can “borrow” against thisstate in order to make further wagers on the game with this borrowedmoney.

The amount needed to bet in order to put the player into a guaranteedwinning position can be computed as follows. First, note that the netwin for either or both sides can be computed by the following formulas:

Net left win=(Σleft bet on square n*left payoff for square n)−total bet;

Net right win=(Σright bet on square n*right payoff for square n)−totalbet;

If the player wishes to bet on the leftmost side and needs to be in aguaranteed pushing (or winning) position, then the net leftmost win canbe set to zero (or greater) and the “left bet on square n” can be solvedfor, wherein n is the current location of the puck. For example,consider operation 5 of the example above. Suppose it is to be computedhow much the player needs to bet to be guaranteed to break even.

Currently, as per the wager in operation 2, the game has one wager of $5on the leftmost side made at position R. Thus, using the payouts forthis particular example as described above, the net left win is:0*(4/3)+0*(2)+$5*(4)=$15 (note that 1 is added to the payout to accountfor the return of the original bet, i.e. a 1:3 payout is represented as4/3 in the above formula). The player wishes to make a bet on therightmost side in order to guarantee a breakeven situation. Thus, letX=the amount needed to bet to guarantee a breakeven situation. Thus, weset the net right win to be 0 (a push if right wins), such that:

0=0*(4/3)+0*(2)+X*(4)−total amount wagered;

The total amount wagered is going to equal the current amount of bets onthe game ($5) plus X. So follows the following equation:

0=X*4−(5+X);

solving for X, we get X=5/3 or $1.67. Thus, the player would need towager at least $1.67 on the rightmost side in operation 5 in order tobreak even (or slightly better). This amount can be rounded (up or down)to the closest denomination allowed by the game to be bet.

In an embodiment, an operator may wish to allow the player to wagerusing borrowed funds only for situations where the player puts himselfor herself into a guaranteed winning position. This way the funds aresure to be paid back. In this embodiment, the above formulas/methods canbe used to determine when the player will be in a guaranteed winning (orbreakeven) position. For example, in one embodiment, money can be loanedto the player as long as both the left net win and the right net win arepositive (or at least zero). In this manner, the player cannot losemoney on the wager even though the player has borrowed funds in which todo so.

In a further embodiment, the game may automatically compute a wagerdirection and amount to wager which would guarantee to put the player ina winning (or break even) position, and output this information to theplayer. For example, in the example above, an optional pop-up window canappear saying, “if you bet $1.67 on the rightmost side, you will beguaranteed not to lose.”

Table II below corresponds to the game form Table I and illustrates anexample where equity funds are used and the balance between the player'sfinds (liquid cash present in the machine) and equity funds (funds theplayer can borrow).

TABLE II player's Equity funds Equity funds Operation funds left sideright side 0-2 $5 $0 $0 3 $0 $0 $15 4 $0 $0 $15 5 $0 $0 $10 6 $0 $0 $5 7$0 $0 $0 8 $0 $40 $0 9 $0 $40 $0

The player starts with only $5 in credits (e.g. the player deposited a$5 bill in the machine) and places a $5 wager in operation 2. Inoperation 3, because the puck has moved in the direction of the initialwager (left), the player can now bet $15 on the rightmost side. This isbecause the player will be guaranteed to win (or at least break even) bynow betting on the right side. When the player reaches operation 8, theplayer can now wager $40 on the left side using equity funds, becausethe house cannot lose by making this loan.

The player may be given the option of whether to use the player's ownfunds or borrowed funds for making wagers (if the current circumstancesdictate that the player will be allowed to borrow money). Alternatively,the player may be forced to use the player's own liquid funds beforehaving to resort to borrowed funds. Alternatively, the player canautomatically use borrowed funds wherever possible before having to usethe player's own funds.

In a further embodiment, bets placed using equity funds may pay theplayer less desirable odds (payouts) for the player than bets placedusing the players own funds. For example, an additional commission maybe taken out of any win based on equity funds. In an embodiment, aplayer may be allowed to place a bet with borrowed funds if the playeris currently in a positive expectation situation.

Alternatively, an embodiment may allow the player to wager on borrowedfunds (on any outcome) without meeting break-even (or profit)requirements. In some cases of betting with borrowed money, the long rundistribution of funds at the outcome of the game will be the same orsimilar whether or not the player makes a wager that does not put him orher into a guaranteed winning position. An example of this is in TableI, operation 5, if the player bet $2.50 instead of $5. Thus, in thesesituations, the house may permit the player to use borrowed funds towager into a non-guaranteed winning position.

FIG. 1 is a flowchart illustrating one example of a wagering game,according to an embodiment. A progression game is a game which has aplurality of game states, each game state may have a different expectedreturn for the player based on the player's wagers and the current gamestate. The game is over when the game reaches a terminating game state.

The method can start at operation 100, which accepts initial bets. Aplayer may not be required to wager on the game before the game starts,and may choose to just wager on the game during the game.

The method can then proceed to operation 102, which progresses the game.This can be accomplished by activating a random number generator inorder to change the game state. The game state may also be changed by aplayer choice (i.e. deciding where to move a piece). A die can be usedto move a piece (or pieces) in the game.

The method can then proceed to operation 104, which checks to see if thegame is over. The game may be over when variable parts of the game state(i.e. piece positions) are in a terminating condition.

If the check in operation 104 determines that the game is not over, thenthe method can proceed to operation 106, which offers the player anopportunity to make additional wagers. The method can then return tooperation 102, which further progresses the game.

If the check in operation 104 determines that the game is over, then themethod can proceed to operation 108, which accounts for wagers. Thismeans taking losing wagers and paying winning wagers according to theirrespective payouts. Any borrowed money can be repaid at this time. Themethod may then optionally start a new game and return to operation 100.

As discussed previously, an embodiment allows the player to potentiallyturn a small or finite amount of money into a large or infinite amountof money by betting with borrowed money based on an equity position inthe game.

FIG. 2 is a flowchart illustrating one example of borrowing money to payfor a wager, according to an embodiment. The method illustrated in FIG.2 may occur during operation 106 from FIG. 1.

The method starts with operation 200, which receives a request by aplayer to make a wager with borrowed finds. The request to use borrowedfunds can be explicitly made by the player, or the request can beautomatically triggered when a player has no more liquid fundsavailable, or the request can typically be automatically triggeredregardless of a player's request of his or her current funds. Theborrowed funds can be used from equity (or “equity funds”) the playerhas developed in the current game in progress.

The method then proceeds to operation 202, which determines if the wagerwill put the player in a guaranteed winning position. This can be doneas discussed above, e.g. determining net wins from all possible outcomesand seeing if all net wins result in a positive net win (or at leastbreak even).

If the check in operation 202 determines that the wager puts the playerin a guaranteed winning (or at least break even) position, then themethod can proceed to operation 204, which allows the player to make thewager. From operation 204, the method can then continue with the game(i.e. proceed to operations 106 or 102).

If the check in operation 202 determines that the wager will not put theplayer in a guaranteed winning (or break even) position, then the methodcan proceed to operation 206 which will reject the wager. The player maythen try another wager, perhaps a different wager that will not berejected as such. Otherwise, the game can continue as normal.

Alternatively, if the check in operation 202 determines that the wagerwill not put the player into a guaranteed winning (or break even)position, then the method can proceed to operation 208, which canautomatically compute a wager amount which would put the player in aguaranteed winning (or break even) position. The newly computed wageramount can then be offered to the player for the player's acceptance, orthe wager can be made automatically. The computed wager amount can becomputed according to the methods described previously. The method canthen continue the game.

Alternatively, if the check in operation 202 determines that the wagerwill not put the player into a guaranteed winning (or break even)position, then the method can proceed to operation 210, which may stillallow the wager but charge a commission on the loan. If a player hasdeveloped a positive expectation in the current game, then the playermay be allowed to borrow against that positive expectation to make afurther wager, even if that further wager will not put the player in aguaranteed winning position. It is noted that the house may neverreceive a payback on this type of loan, for example if the player loses.Typically, the player would not be required to pay such a loan back outof the player's personal funds at a later time. The type of loan for thecurrent game is different from a typical credit loan in which the playermust pay back. Thus, in exchange for making the loan to the player inwhich the house may never get paid back, the house can charge acommission on the loan or can charge an extra commission on any win. Inthis way, when the game is over, if the result is a net win for theplayer, the house receives compensation for making the loan. Typically,the average compensation received should offset the potential losses formaking this type of loan in the first place.

For example, consider the three square game described earlier. When thepuck is on the leftmost square (−1), the player places a $50 wager onthe rightmost side. The puck then moves to the rightmost square (+1).The player now has an expected profit of $100. Of course, the playercould still lose as well. In an embodiment, the house may choose to loanthe player money to make a wager on either side, even though the loanwill not put the player in a guaranteed winning position. The“collateral” for the loan is the player's $100 expected profit. The“interest” for such a loan can be a commission taken out of the player'swinnings. For example, if the player borrows $10 to now make a bet onthe leftmost side, if the puck finishes on the rightmost side the playerwins net $140, while if the puck finishes on the leftmost side theplayer loses $20. A commission can be taken out of the player's winnings(e.g. 20%, or other percentage) to pay for the loan (while if the playerloses he does not owe the house money). In this way, the house willstill profit from making such loans in the long run. The commission rateshould preferably (although not required) be set so that the commissionoffsets the house's potential loss on the loan such that the house willmake more money from making such loans than not making them. In anembodiment, a commission need not be charged.

Thus, according to embodiments, a player can start with a small amountof money, but continue to make wagers while playing the game allowingthe player to build up a large amount of wagers and net wins on thegame. The amount of wagers placed can exceed the amount of liquid fundsthe player currently has. Once the game ends, the player is paid and any“loans” are paid off.

In a further embodiment, the equity concept described herein can beapplied to craps. Equity obtained in a game of craps can be cashed in.For example, consider if a player bets an initial don't pass line bet of$100. The outcome of the come out roll is 10 (“the point”). According tothe standard rules of craps, if the next roll is 10 the player loseswhile on a 7 the player wins (any other outcome of the dice results in are-roll). Since a 7 is more likely than a 10, the player has a positiveexpectation at this point. If the player wishes to surrender this bet,his surrender value is:

(original bet)+(chance of winning*amount to be won)

In this example, the chance of the player winning in this case is (1/3),while the player will win even money on his or her craps bet of $100.Thus, the value of the player's bet is $100+(1/3)*$100=$133.33. Thus,the player can chooses to continue rolling (and win or lose) or acceptthe surrender value of $133.33, which is based on equity in his positionbased on events that have occurred in the game (the come out roll). Allother situations in craps can be addressed similarly (i.e. other comeout rolls, etc.)

The embodiments described herein can also be used to bet on sportingevents, either at intervals on individual games or series of games. Forexample two teams can play a best 4/7 series. After each game in theseries (and even during particular games), payout odds for each teamwinning the series can change to reflect the current conditions (asdescribed herein and/or known in the art) and players can make wagersduring the series.

The embodiments described herein can further be applied to a race game,wherein a player wagers on which of a plurality of pieces will reach afinish line first. For example, a player who wagers on a first piece atthe start of the race (in this case where each piece starts at the sameposition with equal advantage) and the first piece takes the lead, thenat that interval the player has developed equity in the game, which canbe used as a basis to borrow for further bets. In alternative races, thepieces may not have to start at the same location, and pieces may notall have equal advantage (e.g. different pieces may have differentspeeds or dies).

The embodiments described herein can further be applied to a chase game,wherein a player wagers on which of one or more pieces will reach adynamic finish line first. The dynamic finish line is a finish pointwhich can change and can for example be another moving piece.

In addition to applying the equity concepts described herein to theabove-described games, the methods described herein of using equityfunds can also be used for any game that has variable states and is notover without an interval in between states.

In a further embodiment, implementing a wagering game as describedherein can be combined with other gambling games such as craps orroulette. For example, a roulette game can also have a section dedicatedto wagering on a bidirectional linear progression (as described herein).When the ball stops on black, a puck can move in one direction (e.g.left), while when the ball stops on red, the puck can move in theopposite direction. In this way, this wagering game can operatealongside a standard roulette game, with no additional random numbergenerator needed. Alternative, the bidirectional linear progression canoperate alongside a craps game, using predetermined die or dice outcomesto determine which direction the puck moves.

When the player is playing a game in which the player can be “winning”before the game is over, the player may wish to have a way to cash in onthe winning state before completing the game. For example, if a playerbets on a particular horse in a horse race, and the particular horse iswinning, the player has some satisfaction (at least for the moment) thatthe player is in a good position. Of course, the player's horse can loseand the player can be left with nothing. A player may find it attractiveto be able to accumulate (or “bank”) a portion of a positive expectationsituation for later redemption. In this manner, even if the playerultimately loses his or her wager, the player has not lost everythingbecause the banking has been performed.

For example, consider a $100 craps wager on the Don't Pass line. Sincethe house edge on the Don't Pass line is 1.364%, the expected value ofthe player's wager is $98.64. The dice are rolled and the come out rollis a 10. The player is now happy, as the player wins if the shooterrolls a 7 and loses if the shooter rolls a 10 (any other total theshooter keeps rolling). Of course, it is easier for the shooter to rolla 7 than a 10. The probability of the shooter rolling a 7 before a 10 is66%. Thus, the expected win is $133.33. Of course, the player can stilllose the wager if the shooter rolls a 10. The player can surrender hiscraps bet for $133.33 or a lesser amount (so that the house takes acommission). For example, the house can let the surrender the wager for$125. The house makes money on this proposition, and the player gets thepeace of mind of the sure win.

The player can also bank a portion of the expected profit the player hasearned for later use. This can be done in a number of ways. The playercan receive a $33.33 amount (or an amount based on this such as a lesseramount such as $25 to account for a house commission) and the point canbe reset so that the game is in the previous game state with the $100still wagered on the Don't Come line. Alternatively, the house can takea portion of the player's wager (such as 10%), so that the player nowhas $90 on the Don't Pass line. The taken portion can be stored forlater redemption by the player. The $10 taken actually has an expectedvalue of $13.33. This $13.33 (or a number based on this to account forthe house commission) can be accumulated and disbursed to the player ata later time (either later at the instant game, or later at anothergame, or by electronic redemption). If the shooter rolls a 7, the playerthen wins $90 and if the shooter rolls a 10 the player loses his wager.However, in both cases, the player has banked the banked value for alater redemption. In this way, the player can continue to wager, butlimit his losses by ensuring that some amount is still saved for later.

Consider a bilinear progression type game wherein a player can bet on apuck reaching a left side or a right side; the game has five spotsnumbered from left to right: −2, −1, 0, +1, +2 for the puck (notincluding an area to the left of spot −2 when the left side has won andan area to the right of spot +2 when the right side has won); the puckstarts on spot 0; a die is rolled to determine whether to move left orright, the die has six sides: −2, −1, −1, +1, +1, +2; from spot −2, leftpays 1:5 and right pays 4:1; from spot −1, left pays 1:2 and right pays9:5; from spot 0 left pays 19:20 and right pays 19:20; from spot +1 leftpays 9:5 and right pays 1:2; from spot +2 left pays 4:1 and right pays1:5. It is noted that these rules are just exemplary and of course anyother set of rules/parameters could be used as well.

If the puck is on spot +2 and a $10 wager is placed on the left side,and then the die is rolled results in a −2, the puck is now on spot 0.The player now has an expected profit of $15. This can be computed bymultiplying the probability of reaching the left side (50%) by the totalwin of the left side ($50), and then subtracting the original wageramount ($10). The player may wish to “bank” this expected profit forlater use. If the player wishes to bank this amount (or a fraction ofthis amount), the game state should be adjusted back to remove theamount of player advantage that is banked for later use.

Thus, for example, if the player wishes to bank his or her $15 expectedprofit, the game state can return to the previous state (e.g. the puckis at +2 with a $10 wager on the left side). This state is lessdesirable to the player, since the player has no expected profit here.In exchange, the player has banked the $15 in expected profit for lateruse.

The expected profit banked for later use can be used in a variety ofways. The $15 in the above example can be redeemed by the player forcash. The $15 can also be used to buy positive game states at a latertime. For example, if the player is playing a game with multiple gamestates, and the player wants to put himself in a more favorable state,the player can use the banked money to buy a better state. A valuestored for later use can also be applied towards room, food and beveragebills, etc. The value stored for later use can also be redeemed for cashat a later time. The value can also be redeemed for cash instantly, andthe redeemed cash can be immediately returned to the player's currentcredit meter. The value stored for later can be stored locally and/or ona database which can be accessed at a later time.

As a further example, when a player achieves a positive expectation (orprofit) in a game, the player can be alerted and/or presented with a popup window which can make an offer such as, “would you like to revert tothe previous game position and receive a free lunch at the buffet worth$15?”

The player can use value stored to purchase better game states than theplayer currently has. For example, if the player's current game statehas a current value of $20, then when the game state is advanced (e.g.rolling of a die, spinning a wheel, generating random numbers on acomputer, etc.) the game has a current value of $10 (the new game statewas unfavorable to the player compared to the previous game state). Theplayer can use value that the player has banked at a previous time topurchase the better ($20) game state, or any other game state which isimproved over the current game state. So for example, if the player hasbanked a $15 value for later use, and the player has just lost $10 inhis or her current game state, the player can apply $10 of stored valueto put the game state back to the previous state before it lost $10 invalue. The player would then have $5 value remaining which can be usedlater on for further such transactions.

FIG. 3 is a flowchart illustrating an exemplary method of storingpositive expectations for later use, according to an embodiment.

The method can start with operation 300, which plays a wagering game.The wagering game should be one which has multiple game states, eitherdiscrete (each successive game state is prompted and advanced by theplayer) or continuous (the game automatically advances throughout gamestates until a player takes an affirmative action to freeze the currentgame state and take action).

The wagering game can be any wagering game with multiple game states,including but not limited to any of the games described herein or inprior documents incorporated by reference.

The method can continue to operation 302, which determines whether thecurrent game state has a positive expectation for the player. If thecurrent game state has a positive expectation for the player, then theplayer has “equity” in the game.

The player's expectation in a game can be determined in numerous ways,such as:

For all outcomes, Σ(probability of outcome*reward for the outcome).

The previous amount can also be subtracted by the current amount wageredto determine an expected profit in the current game situation. Eitherthe expectation or expected profit can be used in the computationsdescribed herein.

If the current game state has a positive expectation (or positiveexpected profit) for the player, then the method can proceed tooperation 304, which then determines whether the player chooses to bankhis or her positive expectation. This can be prompted by an automaticpop up window which allows the player to choose whether he wishes tobank some or all of his recent gains in expectation for later redemption(with a return of the game state to the prior or other position withlesser expected value than the current state). The player can alsoexercise this option either verbally to a live dealer or electronicallywith a press of a button which allows the player to bank his or herpositive expectation.

If the player chooses in operation 304 to bank his or her positiveexpectation, then the method can proceed to operation 306, which storesthe value the player has banked for later use. This can be stored in thecurrent machine and/or a remote database for later retrieval. A playercan bank his or her positive expectation for later retrieval when theplayer is playing a same or different game at a later point in time.

Either the player can select how much positive expectation to bank, orthe machine can automatically calculate an amount of positiveexpectation to bank. For example, one way to calculate the amount ofpositive expectation to bank is the amount of positive expectation theplayer has gained from the previous game state.

From operation 306, the method can proceed to operation 108 whichchanges the game state to a game state with a reduced positiveexpectation for the player. The difference in expectation between thechanged state and the prior state can be based on the value stored inoperation 104. For example, the game state can revert to the prior gamestate before the last state change, and the value stored can be based onthe difference in expected value between the two states.

The value stored can also be adjusted for a house commission. Forexample, if the player is at game state A (with an expected profit of$15), and the game progresses to game state B (with an expected profitof $25), then the player may wish to bank $10 for later use. The gamestate can then return to game state A, with $10 added to the player'sstored banked value. The $10 can be multiplied by a house commission,for example 0.90. Thus, $9 can be stored for later use by the player.

Thus, by implementing the method as exemplified in FIG. 3, a player canplay a multiple state game and bank value for later use. The player mayend up losing instant money on a final result of the multiple stategame, but nevertheless may have accumulated value which he or she bankedfor later use in which the overall play for the player may be consideredprofitable (for example exceed the player's total investment in thatgame).

In exchange for storing a value redeemable for later use, the value canalso be an award of a non-monetary award. For example, a player mayreceive a free meal, room, or any type of room, food, or beveragecredit. For example, after a game state is changed to a more favorableposition, and the different between the two positions is worth a valuecomparable to a free meal at the buffet, a pop up screen may appear,“Player—press this button if you would like to revert to your previousgame state and receive a free meal at the buffet.” If the player takesadvantage of the offer, then the award (such as a free meal) can bemailed to the player or the player can redeem the award in person (e.g.at the buffet counter, a casino host, etc.) The marketing computer canstore the fact that the player has won the award.

In a further embodiment, a cumulative value of saved awards can beredeemed at a later time for a higher amount than originally earned. Forexample, if a player earns $10 during a game to be stored later, the $10can be redeemed at a later point in time (e.g. the next day, a monthlater, a year later, or any amount of time) for $11 (or any multiple).In this way, a player may be encouraged to return to the casino at alater time since there will be more money waiting for the player than heor she originally accumulated. Alternatively, saved awards can beredeemed for lower amounts as well. This may be so that the house cantake a commission from these transactions. It is up to the casino'spreferences to determined whether saved awards can be redeemed at ahigher, lower, or same cash value as when they were banked.

Saved awards may also be used to purchase additional game positions. Ina bilinear progression type game mentioned above, if the player made a$5 bet on the right side at the −2 position and the puck is currently onthe +2 position, the expected profit of the game is approximately $15with a net win of $20 on the right side. The player may “buy” a roll of+1, thereby resolving or concluding the progression and winning thegame, for $5, effectively winning the player $15 after considering the$5 buy-in. This can also be considered similar or equivalent to“surrendering” (or “retreating”) the wager in this circumstance, butbuying puck moves does not necessarily have to make the player a winner.Puck positions can also be “surrendered” (or “retreated”, “sacrificed”,or “relinquished”) to less valuable positions for the player, in whichthe player can bank the value of such unfavorable changes in game state.

In yet a further embodiment, when a player achieves a positive change inhis or her expectation, a portion of the increased expectation can beautomatically banked for later redemption.

For example, consider the bilinear progression game described above.Since the current state (the puck on 0) has an increase in expectedprofit of $15 from the previous state (when the puck is on 2), themachine can automatically bank a portion (e.g.) 10% of a wager with apositive expected value for later use. Thus, the machine can deduct 10%of the $10 wager ($1) to leave a $9 wager on the left side. The $9 wageron the left side results in a net left win of $36. The expected profitis now 90% of $15 or $13.50. Thus, $2.50 can be banked for later usesince this is the expected value of the $1 wager that was removed. The$2.50 is computed by (50% chance of winning on the left side)*$5 (winresulting from the $1 including the original $1 wager). Thus, byautomatically removing $1 from the wager that has a positiveexpectation, the player can bank $2.50 for later use (in any mannerdescribed herein).

FIG. 4 is block diagram illustrating an exemplary set of components inorder to implement an embodiment.

A machine game 400 can be any wagering machine game, such as a slotmachine, video poker machine, or machine game which plays any game whichcan have multiple states (e.g. games which a player can wager on aprogression). The machine game 400 can be associated with a comp cardreader 402 in which the player can use his or her comp card to identifythe player.

A database 404 can be used to store values banked for later use. Thedatabase 404 can be accessible by all games in an individual casino or agroup of casinos. Value banked for later use can be stored in thedatabase using the player record.

It is further noted that the methods described herein can be applied toall games, including live table games or live sporting events, describedherein (which includes the games described in the Ser. Nos. 10/754,587,10/410,448 and 10/688,898 documents). For example, in any progressiontype game with multiple states, a player may borrow (or be provided witha bonus with playable credits) money from the house to place guaranteedwinning wagers. In some games it may be necessary to make multiplewagers in order to guarantee a win. For example, in a progression gamewith 3 pieces (A, B, C) in a race or chase to win, if a player haswagered on piece A and is in a positive expectation situation (theplayer has equity), the player may need to wager on both pieces B and Cin order to guarantee a winning position. The house can loan the playerthe money to place these wagers in order that the player is guaranteedto win.

In a further embodiment, a conditional wager can be placed. Aconditional wager is a wager that is placed if a particularpre-condition event happens, and then a conditional wager amount isplaced on a conditional wager event. For example, a bettor may wish toplace a conditional wager on a Yankees/Braves game. The player wishes tobet $10 that the Yankees will win on the pre-condition that the Yankeesare ahead at the end of the fifth inning. The $10 is a conditional wageramount and a Yankee win is the conditional wager event. If the Yankeesare not ahead at the end of the fifth inning, then the conditional wageris not placed.

FIG. 5 is a flowchart illustrating an exemplary method of making aconditional wager, according to an embodiment.

The method can start with operation 500, wherein before the eventstarts, a pre-condition event is received, as well as a conditionalwager event and a conditional wager amount. The pre-condition event mayalso include a time period for the pre-condition, which may be either anactual time (e.g. 1 pm, 4 minutes left in the game, etc.) or a discretesegment of an event (e.g. after the fifth inning, at halftime, etc.) Thepayout odds for the conditional wager event may be known when theconditional wager is placed (typically before the event) or may not beknown at the time the conditional wager is placed. The event may be asporting event (including horse racing, football, etc., simulated bymachine or real), a gambling game (e.g. craps, blackjack, etc.), or evena dramatic work (such as a reality show).

From operation 500, the method can proceed to operation 502, whichbegins the event and records the event states. The event states can berecorded on a digital media, on video capture, etc.

From operation 502, the event can proceed to operation 504, whichfinishes the event.

From operation 504, the method can proceed to operation 506, whichdetermines whether the pre-condition occurred. If the pre-condition didnot occur, then the method can proceed to operation 308, wherein theconditional wager is not made. The amount for the conditional wager maybe returned in its entirety, or the house may get a commission on thewager even though it was technically not “in action.”

If the determining in operation 506 determines that the pre-conditionoccurred, then the method can proceed to operation 510 which determineswhether the conditional wager event occurred. The conditional wagerevent is the actual event that the player hopes to occur in order to winthe conditional wager. This can be whether a particular team or horsewins an event, a proposition wager within that event, or any outcomethat the player has wagered on.

If the determining in operation 510 determines that the conditionalwager event did not occur, then the method proceeds to operation 512wherein the player loses the conditional wager.

If the determining in operation 510 determined that the conditionalwager event has occurred, then the method proceeds to operation 514wherein the player wins the conditional wager. The payouts (odds) forthe conditional wager may be determined before the event, or they may bedetermined after the event using for example pari-mutuel determinedodds.

It is noted that the operations in FIG. 5 can be performed in any order.For example, operations 506-508 can be performed before operation 504(when the event ends).

An advantage of participating in conditional wagering is that the bettormay be able to put himself in a no-lose situation if the pre-conditionoccurs. For example, consider a two horse horserace with the horse A asa 9:1 long shot and horse B paying 9:10. A bettor wagers $100 on horse Ato win the race. The bettor also makes a conditional wager, thepre-condition being that horse A be in the lead at the half-way pointand the conditional wager event is that horse B wins the overall race(the odds of B winning should typically be determined based on theconditions at the halfway point).

The conditional wager amount can be set by the player or can beautomatically determined to be an amount necessary to guarantee theplayer a win. At the halfway point, odds can be determined for theoutcomes. This can be done on a pure mathematical basis (if the event isdetermined purely by chance), on a pari-mutuel basis, using ahandicapper, or any other method. If the payout for B winning is 5:1(since A is in the lead it is more unlikely for B to win now), thensince there are only two horses in this example the probability of Bwinning (based on the payout assuming no house, commission forsimplicity) is approximately 17% (1/6) and the probability of A winningis 83% (100%-17%). A $100 wager on B would pay $600. Since the playerhad wagered $100 for A to win and the payout for this bet is $1000 (at9:1), the expectation of this wager is 0.87*$1000=$870. $10 can now beremoved from the original wager amount of $100 on horse A to result in a$90 on horse A, and this frees up $87 (10/100)*870 to place anadditional wager. In other words, the current payouts based on thecurrent state can be used to determine a current value of already placedwagers. The additional wager can now be on horse B which is now paying5:1, which thus pays $600 if horse B now wins, although of course theplayer would lose his original wager on A. If horse A wins, the playerhas won $783. The exact amount can be chosen by the player, can berandomly determined, can be calculated to be the minimum amount requiredto put the player in a break even position, or can be (automatically ormanually) chosen to spread the player's equity over both sides.

Thus, using conditional wagering, the player may be able to put himselfinto a guaranteed winning condition if the player's precondition(s) aremet and the payout odds are such that they can support such guaranteedwagers.

In a further embodiment, a player can use equity in a current wager inorder to place an additional wager. For example, before the game, abettor may bet $100 that the Yankees will beat the Braves outright in aneven money bet (+100 moneyline). After the fifth inning, the Yankees arewinning by 4 runs. At that point in time, the bettor has equity in hiswager. The wager has equity in that the bettor may not be guaranteed towin but he or she has a positive expectation in the wager based on thecurrent game state. The probability of the bettor winning his or herwager multiplied by the win amount is greater than the initial wageritself. If a pari-mutuel system (or a handicapper) at that pointdetermines that that the Yankees now have a 66% chance of winning thegame, the expected value of the bettor's wager is now effectively $132.The bettor may wish to use equity in his or her wager to place furtherwagers. The player may wish to use $1 of that amount and make a secondwager, for example on a proposition that the game will go into extrainnings. A $1 amount is actually worth $1.52 of the first wager($1/0.66). Therefore, $1.52 can be subtracted from the $100 originalwager to result in a $98.48 wager remaining on the Yankees. Now $1 isfreed up for a second wager. It is also noted that the player need notbe in a positive expectation situation in order to utilize the method ofcashing in value for a current wager in progress in order to place asecond wager. However, a bettor in a positive expectation situation maybe more eager to make further bets when he or she is winning theircurrent wagers.

FIG. 6 is an exemplary flowchart illustrating a method of using equityin a first wager in progress in order to fund a second wager, accordingto an embodiment.

The method can start with operation 600, which receives a first wager onan event. The event can be a sporting event, a gambling game (e.g. cardgame etc.), or any event that bettors have placed wagers on in the priorart.

From operation 600, the method can proceed to operation 602, whichbegins the event and progresses a portion of the event (but the event isnot over yet).

From operation 602, the method can proceed to operation 604, whichdetermines whether the player has equity in the first wager. The playerhas equity if the player's expected profit is greater than 0, or if theplayer's expected winnings is greater than the initial wager.

If the determining in operation 604 determines that the player hasequity in the first wager, the method can proceed to operation 606,wherein the player can use some or all of his or her equity in order tomake a second wager. The portion of the first wager used for the secondwager can be “surrendered” (or “relinquished” or “withdrawn”) based onits current value so it can be used for the second wager. The amount ofthe first wager used for the second wager can be considered a reductionamount. The reduction amount can be for example a percentage of thefirst wager, a fixed amount, a user-selected amount, etc.

An advantage of doing this while the bettor has equity in the firstwager is that the bettor can put himself into a no-lose situation. Forexample, consider a football game with the Patriots vs. the Giants. ThePatriots are a +900 long shot. A bettor wagers $100 on the Patriots. Athalftime, the Patriots are winning by +28 points. At this point, apari-mutuel halftime betting pool determines that the Giants are now a+1000 long shot. Assuming no house commission for simplicity, a +1000translates into a 10% probability of occurrence of the Giants winning.Thus, the bettor has a 90% chance of winning $900, thus the effectivevalue of the original wager is now 0.90*900=$810. The bettor can nowsurrender $10 of his original wager which is effectively worth $81. This$81 can now be wagered on the Giants which would result in a $810 win ifthe Giants win. The player now has $90 wagered on the Patriots for a winof $810 if the Patriots win. Thus, the player is in a no-lose situationand can relax and enjoy the game without worry.

It is further noted that operation 604 is optional, and in fact, even ifthe player is in a negative expectation situation, the player can stillutilize the method described herein of cashing out a portion of acurrent bet in progress in order to pay for an additional wager.

In yet a further embodiment, a wager can be placed on a horse in a horserace to beat another horse, but irrespective of where the horsesinvolved in the bet actually finish in the race. For example, consider arace with horses A, B, C, D, and E. A player can wager that horse A willbeat horse D to the finish line, but it does not matter whether horse A(or D) wins the race or where they finish. The payouts for such a betcan be determined using any known method of determining payouts (e.g.pari-mutuel, etc.) This type of wager can also be applied to otherevents as well, such as whether player A may score higher than player Bin a tournament (e.g. tennis, Texas-Holdem, etc.) irrespective ofwhether these players actually win the tournament.

It is further noted that any of the games/methods described herein canbe applied with a “reverse” feature. For example, when a hunter piece (apiece that is chasing a hunted piece) is moving around a track, thehunter piece can change directions. This can be triggered in a number ofdifferent ways, such as by a random number generator, by the hungerpiece reaching a certain location, etc. Thus, for example, if hunterpieces X and Y are chasing hunted piece A around a circular track, pieceX may suddenly change direction and continue in the opposite directionin the hunt for piece A. In a further embodiment, more than one piece,or all pieces, can change direction (which can include both a hunterpiece and a hunted piece).

It is a further feature that any of the games/methods described hereincan accommodate an “escape” feature. If a hunter piece is hunting twohunted pieces, the two hunted pieces may manage to escape from theplaying field. For example, if the hunted pieces get too far away fromthe hunter piece, or if one or more hunted pieces reaches a certainlocation, or by use of a random number generator. If the hunted piecesescape, then the game results in a tie or a further bonus game can beinitiated.

In a further embodiment, game states can be exchanged for a differentpaytable. For example, if a player is playing a multiple state game andthe game progresses into a positive expectation situation for theplayer, the player can exchange the positive game state for higherpayouts. Thus, the game state can be changed to a reduced expectationgame state (e.g., the player will be expected to make less money thanthe prior game state), but in return the player can be presented withhigher payouts (e.g., a paytable) on live wager(s) already placed.

FIG. 7 is a flowchart illustrating an exemplary method of adjustingpayouts based on a change in game position, according to an embodiment.

The method can begin with operation 700, wherein the player plays amulti state game. This can be done as known in the art and describedherein.

The method can then proceed to operation 702, which determines whetherthe current game state has a positive expectation for the player.

If the determination in operation 702 determines that the game state hasa positive expectation for the player, then the method can proceed tooperation 704, which determines whether the player wishes to trade thepositive expectation game state for a different (improved) paytable. Theplayer can indicate his or her desire to perform such trade by verballyspeaking to a dealing, indicating his or her desire on an electronicinput device (e.g., touch screen, keyboard, etc.) If the player does notwish to trade his or her game state, then the method can return tooperation 700, which continues to play the game.

If the player in operation 704 decides to trade his or her game statefor a different paytable, then the method can proceed to operation 706,which changes the game state to a reduced player expectation game state.This can be done by moving piece(s) on the playing field to a positionless favorable to the player. Of course, this is not in the player'sadvantage to do this without some sort of compensation to the player.

From operation 706, the method can proceed to operation 708, whichadjusts the paytable in the game. This is done to compensate the playerfor the change in game state effectuated in operation 706, whichtransforms the game playing field into a less desirable situation forthe player (not consideration the paytable). Thus, in operation 708, thepaytable will be increased (improved) so that the player will win moreif the player ultimately wins a payout from the game being played inoperation 700.

For example, consider a bidirectional linear progression game, wherein apiece moves in either of two opposing directions, wherein the game endswhen the piece reaches either a leftmost side or a rightmost side.Consider the following exemplary conditions (of course other types ofgames and conditions can be used besides the one in this example): thereare three squares (numbered −1, 0, +1) with finish squares to the veryleft and right, with one piece moving in either linear direction (leftor right) based on a roll of a six sided die (with sides −1, −1, −1, +1,+1, +1, or L, L, L, R, R, R). If the die rolls a −1 (or L), then thepiece moves one square to the left. If the die rolls a +1 (or R), thenthe piece moves one square to the right. When the piece reaches to thefinish square left of the leftmost square, or to the finish square tothe right of the rightmost square the game is over and either left orright has won. When the piece is on the −1 square, betting on right pays3:1 and betting on left pays 1:3. When the piece is on the +1 square,betting on right pays 1:3 and betting on left pays 3:1. When the pieceis on the 0 square, betting on left or right pays 1:1. Of course thenumber of squares, parameters of the die, payouts, etc. can be set towhatever the game designer prefers. Further, note that for simplicitythis variation has no house edge, although of course a house edge can beworked into the game.

Consider the piece starts at the +1) position and the player places a $5wager for the piece to reach the left side. After the die (or otherrandom number generator) is activated, the piece ends up moving to theleft. From Table I, operation 3, the player now has an expected profitof $5. If the piece reaches the left side, the player will win a 3:1payout (see Table III, pay schedule A).

TABLE III Pay schedule pay schedule payschedule Event A B C Puck on +1,reaches left 3:1 6:1 3:2 Puck on 0, reaches left 1:1 2:1 1:2 Puck on −1,reaches left 1:3 2:3 1:6 Puck on +1, reaches right 1:3 2:3 1:6 Puck on0, reaches right 1:1 2:1 1:2 Puck on −1, reaches right 3:1 6:1 3:2

Thus, the player now has a game state which is in a positive expectationfor the player. The player may wish to continue to play as normal, orthe player may wish to trade in the game state for a better paytable. Ifthe player chooses the latter option, the piece can move back to the +1position (instead of the 0) position. Now it is more unlikely for thepiece to reach the left side which would result in the $5 wager winning.The pay schedule can now be changed from pay schedule A to pay scheduleB. Thus, the original $5 wager will now win a 6:1 (from Table III, payschedule B) payout ($30) if the piece reaches the left side and wins.

A player may wish to exchange a positive game state for a betterpaytable if the player is interested in a more exciting game with theopportunity to win higher payouts. Typically, if the paytable ischanged, the revised paytable would only apply to a single wager (ormultiple wagers) that are already placed before the paytable is changed.After the paytable is changed, typically, new wagers will still pay onthe original paytable. This is because, if new wagers were paid outusing the higher paytable, the player may get an unfair advantage on newwagers. Therefore, if the player has reverted the game state andreceives pay schedule B (from Table III) on a prior wager placed, then anew wager placed on the game in progress would still pay at pay scheduleA (unless another trade/exchange in operation 704) is performed. Thus,different wagers on the table can be paid using different paytables (payschedules).

In a further embodiment, the player may be allowed to trade a game statethat does not have a positive expectation for a better paytable. Thiscan be performed in the manner described herein. An expectation for agame state can be reduced in exchange for a better paytable.

In another embodiment, a paytable can be decreased in exchanged for abetter game state. For example, consider the example above, wherein theplayer bets $5 when the piece is on the +1 position that the piece willreach the left side. The player can opt to move the piece to the 0position (which makes the $5 bet more likely to win). In exchange, thepaytable used can be reduced to compensate for the better player gameposition. For example, pay schedule C from Table III can now be used.Thus, if the piece reaches the left side (from the 0 position), theplayer will be paid $7.5 (a 3:2 payout on the original $5 wager). Aplayer may wish to make such an exchange if the player is a gambler thatprefers having a reduced risk of losing (even at the exchange of a lowerpayout).

The revised paytables can be computed by determining the value (otherpositive or negative) to the player of changing from a first game stateto a second game state. That value should then be given back to theplayer in the form of the adjusted paytable (either exactly orapproximately). The house may wish to make it to be an even exchange(the player receives the exact expected value on the wager after thetrade that the wager had before the trade), or the house may wish todeduct a commission on the trade (e.g., the modified paytable the playerreceives on the wager results in a smaller expected to the player thanthe prior game state without the paytable modification).

The adjustment in paytable can be computed in many ways, for example asimple ratio between the modified paytable and the new expected valuecan be maintained. For example, consider that a wager has an expectedvalue of A in a first game state and an expected value of B in a secondgame state. Ratio R of game states is B/A. The payouts in the paytablein use originally can thus be multiplied by R in order to determine therevised payouts/paytable when the game state is changed from the secondgame state to the first game state. Further, if the house wishes toprofit from the transaction at all, the revised paytable can be furthermultiplied by a constant less than 1 (e.g. 0.99) so that the housereceives a slight mathematical benefit from the transaction (which maynot be realized in the short run but should be realized in the longrun).

The many features and advantages of the invention are apparent from thedetailed specification and, thus, it is intended by the appended claimsto cover all such features and advantages of the invention that fallwithin the true spirit and scope of the invention. Further, sincenumerous modifications and changes will readily occur to those skilledin the art, it is not desired to limit the invention to the exactconstruction and operation illustrated and described, and accordinglyall suitable modifications and equivalents may be resorted to, fallingwithin the scope of the invention.

1. A method, comprising: performing the following operations on acomputer: receiving a wager from a player on a selected piece out of aplurality of pieces to win a race; conducting a race around a track;randomly triggering a particular piece of the plurality of pieces toreverse direction around the track; completing the race of the pluralityof pieces; and paying the player a payout upon the selected piecewinning the race.
 2. The method as recited in claim 1, receiving asecond wager from the player that a first piece out of the plurality ofpieces will finish the race ahead of a second piece of the plurality ofpieces.
 3. An apparatus, comprising: a computer, programmed to performthe following operations: receive a wager from a player on a selectedpiece out of a plurality of pieces to win a race; conduct a race arounda track; randomly trigger a particular piece of the plurality of piecesto reverse direction around the track; complete the race of theplurality of pieces; and pay the player a payout upon the selected piecewinning the race.
 4. The computer as recited in claim 3, wherein thecomputer is further programmed to receive a second wager from the playerthat a first piece out of the plurality of pieces will finish the raceahead of a second piece of the plurality of pieces.